*Instructor:* Dr. Peter CSIKVARI

*Description:*
The general topic of the course is counting in sparse graphs. The object that we
count (approximately) can be almost anything: matchings, independents sets, spanning
trees, colorings, homomorphisms... The information that we get about the graph can
vary too: we may get the whole graph, or some statistics of the local structure, or the
degree sequence, or we can consider a random graph or a finite subgraph of an infinite
lattice... The tools that we can use is also of great variety: entropy inequalities, zeros of
graph polynomials, correlation inequality and correlation decay, properties of multivari-
ate polynomials (stability), Markov chains, graph covers... A preliminary draft of the lecture note can be found at
http://csikvarip.web.elte.hu/counting_sparse_graphs_lecture_note.pdf
.